Match List-I with List-II.
| List-I (Equation) | List-II (What the equation expresses) |
|---|---|
| (A) \( \Delta_r G^\circ = -nFE^\circ_{cell} \) | (I) Kohlrausch law of independent migration of ions |
| (B) \( E^\circ_{cell} = \frac{2.303RT}{nF}\log K_C \) | (II) Degree of dissociation of a weak electrolyte |
| (C) \( \Lambda^\circ_m = \nu_+\lambda^\circ_+ + \nu_-\lambda^\circ_- \) | (III) Link between the standard emf and the standard Gibbs energy of a cell reaction |
| (D) \( \alpha = \frac{\Lambda_m}{\Lambda^\circ_m} \) | (IV) Link between the standard emf and the equilibrium constant of a cell reaction |
Choose the correct answer from the options given below:
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → A-III, B-IV, C-I, D-II
Two of these equations come from cells and two from the conductance of solutions.
(A) \( \Delta_r G^\circ = -nFE^\circ_{cell} \) — This matches (III) Link between the standard emf and the standard Gibbs energy of a cell reaction. The reversible work done by a cell equals the decrease in its Gibbs energy; with all species at unit concentration this gives ΔrG° from E°cell.
(B) \( E^\circ_{cell} = \frac{2.303RT}{nF}\log K_C \) — This matches (IV) Link between the standard emf and the equilibrium constant of a cell reaction. At equilibrium Ecell = 0, and the Nernst equation then relates E°cell to KC.
(C) \( \Lambda^\circ_m = \nu_+\lambda^\circ_+ + \nu_-\lambda^\circ_- \) — This matches (I) Kohlrausch law of independent migration of ions. The limiting molar conductivity of an electrolyte is the sum of the contributions of its cations and anions.
(D) \( \alpha = \frac{\Lambda_m}{\Lambda^\circ_m} \) — This matches (II) Degree of dissociation of a weak electrolyte. For a weak electrolyte such as acetic acid, α at a concentration c is taken as the ratio of Λm at that concentration to Λ°m.
NCERT (2026-27 edition):
2.3.2 Electrochemical Cell and Gibbs Energy of the Reaction – “If the concentration of all the reacting species is unity, then E(cell) = E°(cell) and we have
ΔrG° = – nF E°(cell) (2.16)
Thus, from the measurement of E°(cell) we can obtain an important thermodynamic quantity, ΔrG°, standard Gibbs energy of the reaction.”
2.3.1 Equilibrium Constant from Nernst Equation – “…But at equilibrium, [Zn2+]/[Cu2+] = Kc… In general,”
\( \displaystyle E^\circ_{(cell)} = \frac{2.303RT}{nF}\log K_C \qquad (2.14) \)
2.4.2 Variation of Conductivity and Molar Conductivity with Concentration – “…he enunciated Kohlrausch law of independent migration of ions. The law states that limiting molar conductivity of an electrolyte can be represented as the sum of the individual contributions of the anion and cation of the electrolyte. … In general, if an electrolyte on dissociation gives ν+ cations and ν– anions then its limiting molar conductivity is given by:”
\( \displaystyle \Lambda^\circ_m = \nu_+\lambda^\circ_+ + \nu_-\lambda^\circ_- \qquad (2.25) \)
“…At any concentration c, if α is the degree of dissociation then it can be approximated to the ratio of molar conductivity Λm at the concentration c to limiting molar conductivity, Λ0m. Thus we have:”
\( \displaystyle \alpha = \frac{\Lambda_m}{\Lambda^\circ_m} \qquad (2.26) \)